The investigators propose to develop techniques for genetic analysis of complex diseases in pedigrees of arbitrary structure and size. As a rationale of the study, they state that diseases such as hypertension, cancer, and psychiatric illnesses have both environmental and genetic components. However, identification of genes contributing to increased risk of such diseases has been difficult, and computational limitations have constrained the use of the available data. The combination of current computer technology and novel simulation approaches to statistical estimation have made timely the development of Markov Chain Monte Carlo (MCMC) methods for genetic analysis of complex traits in pedigrees. Over the past seven years this group of investigators used this approach to develop methods to localize genes and to fit models for genetically complex traits. Extensions of the MCMC methods in several areas are the overall goal of this present application. As data at multiple genetic markers across the genome become increasingly available, more computationally and statistically efficient methods will be developed for joint analysis of data from dense genome screens on individuals among whom there may be multiple complex relationships. Analyses will include studies of allelic associations in multilocus haplotypes at the pedigree and population levels, and their impact on linkage detection and fine-scale mapping. Where marker and phenotype data are available on members of an extended pedigree, current methods will be extended to handle additional trait measures such as multivariate and ordered categorical phenotypes, to incorporate more complex patterns of censoring, and to allow for missing covariate information. Methods will also be developed to analyze map accuracy, recombination heterogeneity, and genetic interference. The impact of map uncertainty and heterogeneity on the localization of genes contributing to complex traits will be assessed, as also will the effect of incorporating a more general meiosis model allowing for genetic interference. Methods will be evaluated by analyses on several simulated and real data sets, including pedigrees segregating Alzheimer's disease, alcoholism, and prostate cancer. These real data sets include several on which are available genome-wide marker screens or more localized multigene haplotypes. Finally, software will be developed that implements these methods, and will be documented and released for use by practitioners in the field.